Breakdown of Anderson localization of interacting quantum bright solitons in a disorder potential

The center of mass of a bright soliton in a Bose-Einstein condensate may reveal Anderson localization in the presence of a weak disorder potential. We analyze the effects of interactions between two bright solitons on the Anderson localization phenomenon. Perturbation calculus shows that even very weak interactions modify localization properties of the system eigenstates. For stronger interactions, i.e. when the solitons are close to each other, the localization is totally broken. It implies that in order to experimentally observe the Anderson localization effects, a single bright soliton has to be prepared and excitation of soliton trains must be avoided.